P32 No. 145 C33

 P31 P32 Axes Coordinates Wyckoff positions Axes Coordinates 3a I Maximal translationengleiche subgroups [3] P1 (1) 3 × 1a [3] P1 (1) II Maximal klassengleiche subgroups Enlarged unit cell, isomorphic [2] P32 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2 × 3a [2] P31 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) (145) (144) [p] P32 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 3a [p] P31 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) (145) p = prime = 3n - 1; u = 1, . . ., p - 1 (144) p = prime = 3n - 1; u = 1, . . ., p - 1 [7] P31 a, b, 7c x, y, (1/7) z; ±(0, 0, (1/7)); 7 × 3a [7] P32 a, b, 7c x, y, (1/7) z; ±(0, 0, (1/7)); ±(0, 0, (2/7)); ±(0, 0, (3/7)) ±(0, 0, (2/7)); ±(0, 0, (3/7)) [p] P31 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 3a [p] P32 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p = prime = 6n + 1; u = 1, . . ., p - 1 p = prime = 6n + 1; u = 1, . . ., p - 1 [3] P31 2a+b, -a+b, c (1/3)(x + y), (1/3)(-x + 2y), z; 3 × 3a [3] P32 2a + b, -a + b, c (1/3)(x + y), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) ±((1/3), (2/3), 0) [3] P31 2a + b, -a + b, c (1/3)(x + y) + (1/3), (1/3)(-x + 2y), z; 3 × 3a [3] P32 2a + b, -a + b, c (1/3)(x + y) + (1/3), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) ±((1/3), (2/3), 0) [3] P31 2a + b, -a + b, c (1/3)(x + y) - (1/3), (1/3)(-x + 2y), z; 3 × 3a [3] P32 2a + b, -a + b, c (1/3)(x + y) - (1/3), (1/3)(-x + 2y), z; ±((1/3), (2/3), 0) ±((1/3), (2/3), 0) [7] P31 3a + b, (1/7)(2x + y), (1/7)(-x + 3y), z; 7 × 3a [7] P32 3a + b, (1/7)(2x + y), (1/7)(-x + 3y), z; -a + 2b, c ±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) -a + 2b, c ±((1/7), (3/7), 0); ±((3/7), (2/7), 0); ±((5/7), (1/7), 0) [7] P31 3a + 2b, (1/7)(x + 2y), (1/7)(-2x + 3y), z; 7 × 3a [7] P32 3a + 2b, (1/7)(x + 2y), (1/7)(-2x + 3y), z; -2a + b, c ±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) -2a + b, c ±((2/7), (3/7), 0); ±((3/7), (1/7), 0); ±((1/7), (5/7), 0) [p] P31 qa + rb, (1/p)((q - r)x + ry), p × 3a [p] P32 qa + rb, (1/p)((q - r)x + ry), -ra +(q - r)b, c (1/p)(-rx + qy), z; +((ur/p), (uq/p), 0) -ra +(q - r)b, c (1/p)(-rx + qy), z; +((ur/p), (uq/p), 0) p = prime = q2 - qr + r2 = 6n + 1; p = prime = q2 - qr + r2 = 6n + 1; q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 q, r = 1, 2, . . .; q> r; u = 1, . . ., p - 1 [4] P31 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); 4 × 3a [4] P32 2a, 2b, c (1/2)x, (1/2)y, z; +((1/2), 0, 0); +(0, (1/2), 0); +((1/2), (1/2), 0) +(0, (1/2), 0); +((1/2), (1/2), 0) [p2] P31 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) p2 × 3a [p2] P32 pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) p = prime = 3n - 1; u, v = 1, . . ., p - 1 p = prime = 3n - 1; u, v = 1, . . ., p - 1